For a quasi-Fuchsian group, the limit set is a Jordan curve whose complement has two components. The quotient of each of these components by the groups is a Riemann surface, so we get a map from marked quasi-Fuchsian groups to pairs of Riemann surfaces, and hence to a product of two copies of Teichmüller space. A Bers slice is a subset of the moduli space of quasi-Fuchsian groups for which one of the two components of this map is a constant function to a single point in its copy of Teichmüller space.

The Bers slice gives an embedding of Teichmüller space into the moduli space of quasi-Fuchsian groups, called the Bers embedding, and the closure of its image is a compactification of Teichmüller space called the Bers compactification.

A Maskit slice is similar to a Bers slice, except that the group is no longer quasi-Fuchsian, and instead of fixing a point in Teichmüller space one fixes a point in the boundary of Teichmüller space.

The Maskit boundary is a fractal in the Maskit slice separating discrete groups from more chaotic groups.

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• Pictures of Bers slices
• Pictures of Maskit slices
• Maskit slice
• Bers slice for square torus
• Bers slice for hexagonal torus